Topics

• CAPM regression
  • estimate beta for cost of equity capital
• Fama-French regression
  • estimate factor exposures (betas) and alpha for mutual fund performance evaluation

Data for CAPM regression

• Ask Julius to get the monthly Fama-French factors from Ken French’s data library and convert to decimal.
• Ask Julius to use yfinance to get adjusted closing prices for some ticker from Yahoo Finance.
• Ask Julius to downsample the adjusted closing prices to end-of-month and and compute returns as percent changes.

• Ask Julius to change the date type for the Yahoo returns to the monthly period format.
• Ask Julius to merge the Yahoo returns with the Fama-French factors.
• Ask Julius to compute the excess Yahoo returns by subtracting the risk-free rate.
• Ask Julius to drop rows with missing data and to filter to the last 60 months.

Regression

• Ask Julius to regress the excess Yahoo returns on the excess market return.
• Ask Julius to report the regression summary.
• Ask Julius to use seaborn to create a regplot of the excess Yahoo returns on the excess market return.
• Ask Julius to use plotly to create a regplot of the excess Yahoo returns on the excess market return and to include the date in the hover data. Ask Julius to save as html.

Data for Performance Evaluation

• Ask Julius to get the five Fama-French factors since 1970 from French’s data library and convert to decimal.
• Ask Julius to get the MOM factor since 1970 from French’s data library, convert to decimal, and merge with the Fama-French factors.

• Ask Julius to use yfinance to get adjusted closing prices since 1970 for FMAGX (Fidelity Magellan) from Yahoo Finance, downsample to end-of-month, and compute returns as percent changes.
• Ask Julius to change the date type for FMAGX to the monthly period format and to merge with the MOM/Fama-French factor data.
• Ask Julius to compute excess FMAGX returns by subtracting the risk-free rate.

Performance Evaluation

• Ask Julius to regress the excess FMAGX returns on the excess market returns and to report the regression summary.
• Ask Julius to cumulatively multiply (1 + intercept + residual) and to plot the result.

Interpretation

• The regression equation is \[r_t - r_{ft} = \alpha + \beta_1 (r_m - r_f) + \cdots + \beta_6 \text{MOM} + \varepsilon_t\]
• The ellipses represent the other terms \[\beta_2 \text{SMB} + \beta_3\text{HML} + \beta_4\text{RMW} + \beta_5\text{CMA}\]
• These terms (plus \(\beta_6\text{MOM}\)) represent long positions with offsetting short positions.

• Rearrange as \[r_t = \beta_1 r_m + (1-\beta_1)r_{ft} + \cdots + \beta_6 \text{MOM} + \alpha + \varepsilon_t\]

• The part

\[\beta_1 r_m + (1-\beta_1)r_{ft} + \cdots + \beta_6 \text{MOM}\]

is a portfolio of the market, risk-free rate, and other factors that has the same betas as FMAGX.
- It is a benchmark for the performance of FMAGX.

• The part

\[\alpha + \varepsilon_t\]

is the return of FMAGX above the benchmark.

• The average return of FMAGX above the benchmark is \(\alpha\).

• The plot shows how the return of FMAGX in excess of the benchmark has varied over time.